I am having the most difficult time trying to understand a problem with the formula a=pe^rt, where A=amount accumulated, p=principal, r=interest rate, and t=time in yrs.
What principal should be deposited at 7.405% to ensure the account will be worth $18,000 in 11 years

- anonymous

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- anonymous

18,000 = p(1+.07405)^11

- anonymous

So 18,000=(1p+7405p)^11, right?

- anonymous

First step would be to add (1 + .07405) to get 1.07405
Then take that to the ^11

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## More answers

- anonymous

2.194166065

- anonymous

I thought the formula was A= p/e^rt

- anonymous

Good
now you have 18,000 = 2.194166065p
so divide both sides by 2.194166065

- anonymous

8203.572322= p

- anonymous

or $8203.57?

- anonymous

OK.. we can do it your way... just a minute.

- anonymous

18,000 = P e^(.07405*11)
18,000 = Pe^.81455
18,000 = P 2.258
Divide by 2.258
$7971.66

- anonymous

How do you calculate e?

- anonymous

I plugged it into the calculator... I have an e^x key.

- anonymous

Wait just a minute

- anonymous

Also the ln key right?

- anonymous

Ok, I got the same thing you got this time.

- anonymous

I am not used to the e function.. here is an example, I will do yours for you following this example
So 130000 = 1949 e^(.00835 t)
Take logs of both sides:
ln 130000 = ln 1949 e^(.00835 t)
= ln 1949 + ln e^(.00835 t)
= ln 1949 + .00835 t
t = (ln 130000 - ln 1949) / .00835
= (ln 130000/1949) / .00835
which you have to calculate using a calculator

- anonymous

18,000 = Pe^(.07405 * 11)
18,000 = Pe^.81455
ln 18000 = ln P + ln(e^.81455)
ln 18000 = ln P + .81455
9.79813 - .81455 = ln P
8.98358 = ln P
e^8.98358 = e^ (ln P)
$7971.12 = P

- anonymous

ok. It was the "e" part that was throwing me off. But what you and I got is what the book has also.

- anonymous

Great... A little out of my league... but I am glad we got it.

- anonymous

Now, with the formula with A =p(1+r/n)^nt
A = $982500 p+71500, t=17yr

- anonymous

Don't we have to know either r or n?

- anonymous

I have 98, 2500=71, 500(1+r/n)^17. Do you know how I would find r/n?

- anonymous

R is what they are asking for. R is a percent

- anonymous

What is n?

- anonymous

Here's the question:
For compound interest accts, the amount A accumulated or due depends on the principal p, interest rate r, number of compounding per year n, and the time t in years according to the formula A=p(1 + r/n)^nt.
Find the r given A=$98, 250, p=71,500, and t=17 yr with interest compound monthly

- anonymous

compounded monthly means that n = 12

- anonymous

982,500 = 71500(1 + r/12)^12*17

- anonymous

oh, because 12 represent the "per year"

- anonymous

982,500 = 71,500(1 + r/12)^204

- anonymous

divide both sides by 71,500

- anonymous

13.7412587 = (1 + r/12)^204

- anonymous

13.
74128874=(1+r/12)^204

- anonymous

Now you have to get rid of the ^204 you do that by taking the 204th root of both sides. Use the x sqrt(y) key on your calculator

- anonymous

1.012927965 = 1 + r/12

- anonymous

Subtract 1 from both sides

- anonymous

.012927965 = r/12

- anonymous

multiply both sides by 12

- anonymous

12.155 = r

- anonymous

ON the step with the sq rt of 13.7412587 I got an error msg

- anonymous

Your saying 204 sq rt 13.7412587 correct?

- anonymous

You are not taking the sqrt root..
Find the key that has x sqrt(y)
type in 13.7412587 hit the xsqrt(y) key and then type in 204 and hit enter

- anonymous

I dont believe I have that key

- anonymous

Are you operating a TI-84?

- anonymous

NO.. just a calculator on my computer the basic one..

- anonymous

Let me see if I can find a TI-84 on line and tell you what it looks like

- anonymous

How about under MATH option 5 does it show an x and then a radical sign

- anonymous

yes

- anonymous

You want the x to be the 204 and under the radical sign to be the 13.xxxxxx
Try it and see if you can get what I got.

- anonymous

YES!!!! I got it! such a relief! thank you very much

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